13th June, afternoon: The first lines on the map

"So... it's to do with triangles, sir?" Cotton asked, though that didn't explain anything about how you made a map, unless he was understanding it all wrong somehow.

He rested the rifle's butt on the ground again and leaned on it, trying to picture how this all worked. No wonder officers had to know how to read and write!

Edward nodded.

"Yes, it's all about triangles. We will measure out a line here, and then we will take the angle between this line and the line of sight to the target from both ends of that line. And the point where both lines of sight cross each other is the location of the target, be it a hill, a building or a Frenchman."

"But... sir." Pye was very quiet as he spoke. ".....maps are square, why do you need triangles?" All that Torrington had said discouraged the young lad. He thought it was somehow easy to draw a map, but the longer he listened to the Lord, the less he understood and then his mind just forgot what was said before and he could not make neither heads nor tails out of it.

"We need the triangles between the important points on the map", Edward patiently explained. He didn't mind, as long as the men showed interest and the questions were valid. He knew that this wasn't exactly easy for an uneducated man to comprehend; even some men of his own class shied back, as soon as they realized that this was actually geometry; but he firmly believed that once the men had grasped these logical principles, they would profit from them in a general way. That was way he was going to the trouble of explaining the theory instead of only ordering the practical.

"Because if we know the length of the baseline and the angles, I can do some mathematics and work out the length of the other two sides. Then we can take one of those sides as a new baseline and measure a new triangle from there. But that only works with triangles, not with rectangles. And if we can measure distances by sight, that's better than measuring them on the ground with rods, because we can see at one glance points that would take days to reach if you have to lay one measuring rod at the end of the other. Besides, the line of sight is always the shortest distance between two points. Try it out with a piece of string, if you want."

"The, uh, baseline, sir?" Cotton asked, frowning in concentration. "Do you mean that you measure the distance to somethin' - like a church spire, I s'pose - fr'm two diff'rent places?" Because he couldn't see, otherwise, how it could possibly work or what a 'baseline' could be, otherwise.

"So....it's like......if you have a pie but you need to reassemble it again.. couse it's all cut up in little triangles...and to do that, you need to know the sides ter match them together?" No, now that he asked, it made no sense.

"....How do you measure how high a mountain is, sir?.. We cant all stand on it.. ter make triangles."

"Yes, Cotton. Exactly. It will make even more sense in a few minutes, when we try it out for real."

He had a bit more difficulty understanding Pye's example, but finally he thought he got it.

"In principle, yes. Just think of the map as one large rectangular pie that has been cut into many small triangles. If you take those two sides that are exactly the same length and put them together, and then find another piece that fits exactly to one side there, and so on, you will finally have a complete pie again. Now we cut the landscape into triangles with our measurements, and later we piece it together on a piece of paper, only on a smaller scale, like a ship model. And for the height of mountains we will use a different trick. I will show you that one later. It has actually to do with triangles as well and the fact that if you keep the angles at the side, but double the baseline, the sidelines double as well."

Cotton looked around, registering the blank looks on the faces of those around him. "Um, sir... d'you mind showin' us that? I mean, sketchin' it out or summat, please? 'Cause I can't pikcher it in me head."

To Pye it suddenly made sense. What they were doing is.. making pie into a smaller pie without loosing it's..well its shape and the way it would look. Somehow that made sense even if he could not remember what the correct word for it was.

"...only... how will we know we've made the same triangle now as before?....we don't have any cut pieces yet.. sir."

Freddy just stood there, held the map as directed, nodded and smiled. The Captain had lost him about three seconds after he had opened his mouth. First he had thought he was talking about fishing, because he had mentioned something like Angeln, then Cotton and Roper had nearly shot at something in a tree, and then Pye had mentioned pies, so perhaps he was going to make a fish or game pie, but he still couldn't see how this was supposed to be related to map making.

Well, perhaps Pye had understood and could explain afterwards.

Edward nodded at Cotton's suggestion.

"Certainly. We'll do a small sketch of the landscape here now, so you can see all the steps, and how they fit together. Pye, Rottländer, you can let go of that map now. Please take those long sticks with the plate atop it from the mule instead."

Freddie did as ordered; or at least, he did what he believed the Captain's words and gestures had meant. The thing he was fetching now was a rather strange thing indeed: three wooden sticks, each nearly as high as Freddie, mounted to a metal head, to which a small plate was attached. There were holes in the plate, and screws all over the thing, and Freddie was very careful indeed not to mess up anything when he handed the thing to Captain Torrington.

Pye followed along with Freddie and took what he had left behind. He was not exactly sure what these were for, but decided that if anything Torrington would be willing to show them.

He studied the other boy questionably. ".....did you... before?" He whispered indicating Torrington and his map.

Cotton watched with interest as Rottländer brought a strange-looking instrument to the Engineer Captain. If Captain Vickery's pistols were expensive, he didn't think he wanted to know what this cost - although he was very interested in finding out what it was for.

But surely the Captain didn't need to get his precious instruments out simply to draw a sketch to explain what he had been talking about?

"Thank you, Rottlaender. And now that larger tablet with the paper attached to it, please."

Edward opened the leather strings that held the tripod's legs together and shook them out with practiced movements, then placed it on a level spot. A few adjustments of the legs, and it soon was stable and level. Then he accepted the plate Freddie was holding and screwed it to the plate on top of the tripod. In future, the placing of the tripod would be the job of one of his assistants, but for now it was quicker if he did it himself.

"Gentlemen, this is what's commonly called a plane table. As you can see, it's nothing special, just table on a tripod, giving a level surface for a piece of paper, but it's one of the oldest surveying instruments known to mankind. It is not the most precise, but it certainly is very quick."

He would use the more sophisticated and precise theodolite later, but to explain things, the old fashioned plane table and alidade was better suited. Besides, even untrained soldiers weren't likely to damage those instruments accidently. He pointed to the sheet of paper that was tacked to the table on the tripot.

"On the paper here we will draw the lines we're going to measure now. All the triangles we'll cut this valley into. The other thing we need to start is our baseline. That is very simply measured."

He took a metal chain, made out of short rods connected with rings, from the mule's back.

"This chain is exactly 66ft long. Two volunteers to measure out our baseline with it?"

Cotton looked at Roper and shrugged. They might as well continue to help out with the officer's demonstrations. No doubt things would become clearer as the afternoon wore on.

"Where d'you want us, sir?" he asked, slinging his rifle across his back so he could have both hands free.

Pye looked ready to help with anything that was needed, as long as he was ordered it. He looked around and then moved to the side. If the older men wanted to lend a hand first, they were certainly having priority in it.

He smiled and observed attentively even if.. it was all still too complicated to understand.

"Just here, on that stretch of grass. It needs to be level and without bushes or other impediments, but the precise spot is not important. Stretch it out, please. Corporal Miller, please check that the chain doesn't get entangled somewhere."

He turned, pulled two wooden stakes and a mallet from the saddle and handed them to Pye and Freddie. One of his eyebrows went up in friendly mockery as he motioned them to follow him to one end of the chain.

"You two will have a chance to work off some of that youthful energy. When they have stretched out the chain, you'll mark the spots where the ends come to rest."

Quite why it had to be sixty-six feet long and no more - or less - Cotton couldn't say.

They had it laid out straight on the ground soon enough and he looked up at the officer, who was passing pegs and mallets out to Pye and Rottlander.

"You hit either of us with them mallets an' you'll be for it," he said teasingly.

"We'd outrun you both, Gabe." Pye challenged back, then grinned at Torrington. A mallet in one hand, a stake in the other he looked ready to set up more than just the marker of one end of the chain.

He was feeling a bit cold now, that his body had cooled a bit due to the wet clothing, but just enough exercise would have him nice, warm and comfortable in no time. "Sir. Will it be one stake per end?" Which would have one boy in need of running the length of the chain to make the mark on the other side.

"Yes, it will, Pye. Cotton and Roper will give it a tug so that it is really stretched out, and then Rottlaender and you will mark the distance. Ideally, the centre of the peg and the middle of the last ring on the chain should be right above each other."

Edward looked up and down the young rifleman, then studied his batman.

"Is there by chance a logical explanation why you two appear to be wet, and not just behind the ears? You didn't seem dusty enough this morning to require such a draconical measure."

His voice was curious, but not in an unfriendly way.

Of course there was a logical explanation why they were wet. "We were in the river, sir. Head to toe...or.. toe to head actually, sir." The boy answered. It was logical that one could get wet in a river, since rivers were wet.

He waited for the two men to tug the chain taut so that it would be as stretched straight as it could be. He'd have gone back to the other end to land the peg, of course. But he needed to know exactly where to land it.

Edward waited a moment longer to give everybody a chance to get ready, then he commanded:

"Pull!"

When the chain was as taut as several pounds of metal would become, he indicated the place where the peg was to go with the tip of his boot.

"Rottlaender, your's goes here. Pye, with me."

He strode quickly off to the other end of the chain.

Cotton took as good a grip on the chain as he could and pulled when the officer gave the word of command. What this had to do with map-making, he couldn't say, but he trusted that all would be made clear. He glanced at the young German Rifleman. "Jus' you be careful when bangin' that in, all right? Don't go knockin' me on the head or anythin'."

"Yes, sir!" Pye answered excited, and scampered after Torrington, carrying his mallet. He grinned back at Cotton. Silly chap thought that they would smack him! They were better than that.

"Gabe, he doesn't understand you, so be careful!" Which was a lie, and both he and Freddie knew it. He knelt down. "Ready sir!"